This is cute, but the use case in robotics is questionable. A variable ratio transmission for a robot seems to solve a problem nobody has. Electric motor control today is able to do that job over a wide torque and speed range. From drones to electric cars to Diesel-electric locomotives, nobody uses variable-speed gearboxes much any more. There are many robot gearboxes, but I've never heard of one with a shifter. Machine Design has ads for robot gearboxes, including ads from Harmonic Drive, but they're all fixed ratio.
This thing would need a second motor to adjust the speed change, with an encoder, plus encoders on the input and output ends of the transmission. Something has to control all that.
If you need sudden bursts of high torque, overload the motor while monitoring temperature. You can run electric motors far above their continuous rating for brief periods, and if temperature is monitored, this is safe. That's how Tesla's "launch mode" works.
Not seeing the use case for this thing in robotics.